It is known that the generic n-th order moment (n being an integer and positive member) of the electromagnetic field of an optical beam is given, in polar coordinates, by the relation: ##EQU1## where I is the electromagnetic-field spatial intensity, q and .phi. are the transverse polar coordinates with origin on the beam axis; q can be the radius (for the near-field) or the angular coordinate (for the far-field).
More particularly, the square root W.sub.0 of the 2nd order moment, i.e. the root mean square of the spatial distribution of the beam electromagnetic field (or of the field at the output of an optical fiber, in the preferred application) represents the beam spot-size.
The knowledge of W.sub.0 is important for the knowledge of the geometric dimensions of the field, which give information both on the collimation of and on the power distribution in the beam.
In the particular case of the optical fibers (to which reference will be made hereinafter since the invention has been mainly developed for application in this field) the spot-size knowledge gives information on propagation properties inside the fiber and on splice losses; this information is indispensable when optical fibers are used in a telecommunications system. Even more particularly, spot sizes both in the near- and in the far-field characterize monomode fibers. In fact splice and bending losses, and cabling losses due to microbending can be obtained from these parameters. Spot-size variation versus wavelength gives cut-off wavelength of the first higher order mode and also the waveguide dispersion.
A number of different techniques have been proposed for spot size measurement in optical fibers.
One of them has been described by R. Yamauchi, T. Murayama, Y. Kikuchi, Y. Sugawara e K. Inada in the paper "Spot-sizes of single mode fibers with a noncircular core" presented at the Fourth International Conference on Integrated Optics and Optical Fiber Communication (IOOC '83, Tokyo, Japan, 27-30 June 1983, paper 28A2-3, pages 39 and ff.). According to this method, spot-size is obtained by determining the value of the intensity I at the fiber at the output by near-field intensity scanning and then by directly applying relation (I), with n=2. This method can be used for measuring moments of any order.
Since the integration interval extends to infinity, but beyond a determined distance from the beam axis the intensity is masked by measurement noise, the method can introduce significant errors into the value calculated. In addition, radial scanning is complex per se.
According to other methods a Gaussian distribution is assumed for the function representing the intensity I and quantities are measured which can be correlated to spot-size by means of formulae, which are valid only if the hypothesis of Gaussian field is satisfied. Examples of such methods are described in the papers: "Direct method of determining equivalent-step-index profiles for multimode fibers" by C. A. Millar, Electronics Letters, Vol. 17, No. 13, June 25, 1981, pp 458 and ff., and "Fundamental mode spot-size measurement in single-mode optical fibers" by F. Alard, L. Jeunhomme, P. Sansonetti, Electronics Letters, Vol. 17, N.25, Dec. 10, 1981, pp. 958 and ff.
Since the hypothesis of Gaussian field applies only in very particular cases, the measurements obtained by these methods present an intrinsic lack of accuracy difficult to be quantized.